The seventh-generation Civic might have sold in record numbers, and it might have ferried millions of people quite happily from Point A to Point B; but nobody would ever have used the words "interesting" or "inspiring" to describe. No, it wasn't until the eight-generation -- 2006 to 2011 -- Civic came along that the Civic got enough real attitude to inspire driving aggressive enough to melt the stock tires off.
The DX, GX and Si models came from the factory with a set of P195/65R15 Dunlop Sport 5000 Symmetrical tires; these tires are mediocre at best, and Tire Rack reports that few people who've had them would buy them again. As of 2013, Tire Rack's best-selling replacement tires for the DX are the Bridgestone Turanza Serenity Plus and Continental PureContact with EcoPlus, both of which are about $10 more expensive than the stock tires, but rate far higher in every category. Fuzion's Touring tires are cheaper than the stock tires, and very popular -- but very loud -- all-around performance replacements.
On the EX and LX, the stock tires are sized P205/55R16. Honda offered both the Bridgestone Turanza EL400-02 and the Goodyear Eagle RS-A. The RS-A is a good performance tire in the dry, but gives up a lot in the rain, and on snow and ice. The Turanza is reviewed as average in most categories, and fairly low in dry traction and treadwear. Consider upgrading to the Serenity Plus, Fuzion Touring or the sporty Kumho Ecsta.
The Civic Hybrid came with a set of either DX-sized Dunlop SP31 A/S tires that rate very low in almost every category that Tire Rack specifies, or a slightly better set of Bridgestone Insignia SE200-02 tires. The Turanza Serenity, Continental PureContact with EcoPlus and Fuzion Touring tires are all better and cheaper than the Dunlops.